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      <title>Zmn Info</title>

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      <template id="header">
         <h3>${MathML.sans('<mtext>Results of &#8220;</mtext>' + MathML.sub('&Zopf;', 'mn') + '<mtext>&nbsp;group&#8221; computation for&nbsp;</mtext>' + group.name)}</h3>
      </template>
      <template id="Z_mn-group">
         <p>A group of the form ${MathML.sans('<msub><mi>&Zopf;</mi><mn>mn</mn></msub>')}
            is isomorphic to the product group
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>m</mn></msub><mo>&times;</mo><msub><mi>&Zopf;</mi><mn>n</mn></msub>')}
            just when ${MathML.sans('<mi>m</mi>')} and ${MathML.sans('<mi>n</mi>')} are relatively prime.
            In this case, because ${m} and ${n} are relatively prime,
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>'+m+'</mn></msub><mo>&times;</mo><msub><mi>&Zopf;</mi><mn>'+n+'</mn></msub>')}
            is isomorphic to ${MathML.sans('<msub><mi>&Zopf;</mi><mn>'+(m*n)+'</mn></msub>')}.</p>
         <p><a href="" class="show-illustration" data-m="${m}" data-n="${n}">Click here</a> to see
            an illustration of why ${statement( m, n, true )}.</p>
      </template>
      <template id="non-Z_mn-group-prime">
         <p>A group of the form ${MathML.sans('<msub><mi>&Zopf;</mi><mn>mn</mn></msub>')}
            is isomorphic to the product group
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>m</mn></msub><mo>&times;</mo><msub><mi>&Zopf;</mi><mn>n</mn></msub>')}
            just when ${MathML.sans('<mi>m</mi>')} and ${MathML.sans('<mi>n</mi>')} are relatively prime.
            In this case, ${MathML.sans('<mi>mn</mi>')} = ${group.order}, which gives no possibilities for
            ${MathML.sans('<mi>m</mi>')} and ${MathML.sans('<mi>n</mi>')}.</p>
         <p>Thus there is not even a product group
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>m</mn></msub><mo>&times;</mo><msub><mi>&Zopf;</mi><mn>n</mn></msub>')}
            to speak of being isomorphic to.  (One of ${MathML.sans('<mi>m</mi>')} or ${MathML.sans('<mi>n</mi>')}
            would need to be 1, making one factor the trivial group, the the other
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>mn</mn></msub>')}.)</p>
      </template>
      <template id="non-Z_mn-group">
         <p>A group of the form ${MathML.sans(MathML.sub('&Zopf;', 'mn'))} is isomorphic to the product group
            ${MathML.sans('<msub><mi>&Zopf;</mi><mn>m</mn></msub><mo>&times;</mo><msub><mi>&Zopf;</mi><mn>n</mn></msub>')}
            just when ${MathML.sans('<mi>m</mi>')} and ${MathML.sans('<mi>n</mi>')} are relatively prime.
            In this case, the factors of ${MathML.sans('<mi>mn</mi>')} are ${facs}, which cannot be divided into
            two non-trivial sets that do not both contain ${factors[0]}.  Thus, there cannot be two relatively prime
            factors of ${MathML.sans('<mi>mn</mi>')} since any non-trivial factors must both be divisible by ${factors[0]}.</p>
         <p>${allOffers(group.order)}</p>
      </template>
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